Phase diagram of the two-dimensional antiferromagnet Ni-5(TeO3)(4)Br-2 with triangular arrangement of Ni2+ (S=1) magnetic moments within the [Ni5O17Br2] subunits has been investigated by temperature and magnetic field dependent heat-capacity, magnetization, and magnetic-torque measurements down to 1.5 K and up to 23 T. A nonzero magnetic contribution to the heat capacity observed up to 2.3T(N) is consistent with short-range magnetic ordering and the two-dimensional nature of the system. Below the Neel temperature T-N=29 K several antiferromagnetic phases were identified. The zero-field phase is characterized by a planar antiferromagnetic arrangement of the two in-layer neighboring [Ni5O17Br2] magnetic clusters within the magnetic unit cell. When the magnetic field is applied along the a(*) crystal axis, a spin-flop-like transition to a phase with a complex out-of-plane arrangement of Ni2+ (S=1) magnetic moments occurs at similar to 10 T. Using a molecular-field approach we predict that this transition will shift to higher fields with increasing temperature and that a magnetic phase with ferromagnetic ordering of [Ni5O17Br2] magnetic clusters will occur above 24 T. We ascribe the richness of the magnetic phases to strongly exchange-coupled clusters, being the basic building blocks of the investigated layered system.